Logarithmic units are abstract mathematical units that can be used to express any quantities (physical or mathematical) that are defined on a logarithmicscale, that is, as being proportional to the value of a logarithm function.

In this article, a given logarithmic unit will be denoted using the notation [log n], where n is a positive real number, and [log ] here denotes the indefinite logarithm function Log().

The motivation behind the concept of logarithmic units is that defining a quantity on a logarithmicscale in terms of a logarithm to a specific base amounts to making a (totally arbitrary) choice of a unit of measurement for that quantity, one that corresponds to the specific (and equally arbitrary) logarithm base that was selected.

Logarithmic graphs are line graphs with one or both axes in a logarithmicscale.

The Y axis is a logarithmicscale, the X axis a linear (arithmetic) scale.

On a logarithmicscale, the actual distance representing a given percentage increase or decrease is the same anywhere along the scale, so a continuous percentage change shows as a straight line rather than a curve.

www.graphicsserver.com /com_products/GraphChoiceLog.aspx (266 words)

Logarithmic scale(Site not responding. Last check: 2007-10-09)

stellar magnitude scale for brightness of star s In the first five examples small values (or ratios) of the underlying quantity will correspond to negative values of the logarithmic measure.

The Logarithmic Time Perception Hypothesis Logtime is the psychochronometric hypothesis that our age is our basis for estimating long time intervals, resulting in a perceived logarithmic shrinkage of our years as we grow older.

The divided gradicule of the theodolite along with the scales provided on the slide rule allow for the use of the tail method for estimate the height of the balloon when strong winds are present (elevation angles of 40 degrees of less).

The upper part of the stock carries two pairs of sine and cosine scales, one pair extending from 0.5 ° to 90° and the other from 10° to 90°; the degrees from 0° to 20° on each cosine scale are marked on a small arc instead of being crowded together as in an ordinary slide-rule.

A logarithmicscale, twice repeated, and identical with part of the slider scales, is also provided on the upper part of the stock; this permits of the rule being used in a limited way as an ordinary slide-rule.

The most common other scale is the logarithmicscale in which the numbers are spaced according to their logarithms.

A logarithmicscale allows us to plot a large range of values without losing the distinction between small values - if our values range over two or more orders of magnitude, but we want to be able to tell 10 from 30 as well as 100 from 300 2.

With a logarithmicscale, numbers are spaced according to the percentage change between values (the change from 20 to 30 is a 50% increase - so is the change from 150 to 225 - the spacing will be the same with a logarithmicscale) 3.

In accordance with the principal embodiments of the invention, cooperating logarithmicscales with indicia corresponding to the parameters target speed, range, projectile speed and lead are horizontally or circularly displayed on a horizontal or circular slide rule type device, the particular indicia and scale units being those most commonly known for the particular parameter.

The arrangements of logarithmicscales and markers which permit successive multiplication and division to be carried out on a slide type calculation are well known in the calculator art and all such arrangements are deemed to be within the scope of the present invention.

The projectile speed scale 212 is disposed along the second circumferential edge 224 of the slide member 206 and the reference scale 216 is disposed on the fixed member at such a distance from axle 214 that the second circumferential edge 224 may be rotated immediately inside the reference scale 216.

Logarithmic multiband color encoding permits direct comparisons of maps, such as maps of different elements in the same field of view or maps of the same element in different areas, because the color scale is identical for all maps.

Logarithmic multiband color encoding is a pseudocolor scale in which three distinct color bands are defined to correspond to major, minor, and trace constituent levels, with a lower threshold of 0.001 used for the trace band since zero must be excluded from a logarithmicscale.

Logarithmic multiband color encoding achieves a strong and easily recognizable color contrast between the classifications, and since no color repeats within the scale, there is never an ambiguity as to which class is depicted at any pixel.

Logarithmicscales give the logarithm of a quantity insteadof the quantity itself.

Some of our senses operate in a logarithmic fashion (doubling the input strength adds a constantto the subjective signal strength), which makes logarithmicscales for these input quantities especially appropriate.

Logarithmicscales are either defined for ratios of the underlying quantity, or one has to agree to measure thequantity in fixed units.

www.therfcc.org /logarithmic-scale-103251.html (252 words)

Introduction to Logarithmic Scales(Site not responding. Last check: 2007-10-09)

The purpose of this series of web pages is to introduce you to the concept of logarithmicscales, and in particular to the decibelscales commonly used in acoustics to measure loudness.

The purpose of the following paragraphs is to explain the difference between a linear and a logarithmicscale and to indicate conceptually why we use logarithmicscales as the measurement method in stimuli/sensation situations such as quantifying loudness.

The key point to understand from the previous example is that the difference between a logarithmic and a linear scale rests on whether the natural steps increase in an additive fashion (linear scale) or in a multiplicative fashion (logarithmicscale).

A logarithmicscale is different in that the ratio of successive intervals is not equal to one.

The decibelscale is a logarithmic ratio scale: we start with a ratio of pressures, then take the logarithm and finally multiply by 20.

Thus the zero point on the decibelscale is simply the point at which the measured amplitude is equal to the reference amplitude.

www.speechandhearing.net /faq/faq1-2.htm (680 words)

logarithmic scale(Site not responding. Last check: 2007-10-09)

Logarithmicscales give the logarithm of a quantity instead of the quantity itself.

In particular our sense of "audition", i.e., hearing, is naturally designed to perceive equal ratios of frequencies as equal differences in pitch.

In the last two examples large values (or ratios) of the underlying quantity will correspond to negative values of the logarithmic measure, because of reversal of the scale by a minus sign in the definition.

Two notes which are adjacent in a scale are said to be a "semitone" apart.

In a 12-note logarithmicscale, the ratio is a constant and must be the twelfth root of two (= 1.05946).

The logarithmic 7-note scale in this demonstration is the "major" scale of Western music comprised of notes generated by multiplying the starting frequency by 1.05946 raised to the 0, 2, 4, 5, 7, 9, 11, and 12 (to complete the octave) powers.

webphysics.davidson.edu /faculty/dmb/Scales/Scales.html (216 words)

Logarithmic scale(Site not responding. Last check: 2007-10-09)

Logarithmicscales give the logarithm of a quantity instead of the itself.

Some of our senses operate a logarithmic fashion (doubling the input strength a constant to the subjective signal strength) makes logarithmicscales for these input quantities appropriate.

Logarithmicscales are either defined for ratios of the underlying quantity or one to agree to measure the quantity in units.

The x-axis is a logarithmicscale, which means that each number is ten times greater than the one before it.

Logarithmicscales do NOT display equal intervals, as do non-logarithmic scales.

You will need to keep this spacing of a logarithmicscale in mind as you complete data tables in two other lessons: "Graphs and the Composition of the Earth’s Thermosphere" and "Graphs and the Composition of the Earth’s Ionosphere".

The logarithmicscale of time perception presented by this model may be only a rough approximation of actual human perception, but is probably a much closer one than the linear scale usually assumed.

The simple premise of Logtime, from which the logarithmic relationship can be derived (see Appendix), is that the human mind judges the length of a long period of time, such as a year, by comparing it with current age.

A consequence of the logarithmic function is that it is the ratio of the years defining an interval of time that we use to judge the duration of that interval, not the absolute magnitudes of those years.

A logarithmic or semi-logarithmic line chart has a logarithmicscale on the y (vertical) axis and an arithmetic scale on the x (horizontal) axis.

In this chart, the female rates for the younger age groups seem somewhat higher compared to the male rates and the percentage differences in the rates for the older age groups are not as evident as in the arithmetic line chart.

In other words, the logarithmic chart points to a possible significant difference between the rates at the younger age groups, whereas in the arithmetic line chart the difference at the younger age groups is lost in the plotting of the higher absolute values for the older age groups.

Logarithmicscales allow a large range of numbers to be compressed into a much smaller one.

Mathematicians express this on a logarithmicscale, which when plotted as a graph is called a "leaning curve".

Just like space, time is often best represented on a logarithmicscale: we know a lot about different decades in the present century, but (to us) one decade in the Jurassic era would be much the same as any other.